In the case corresponding to a selfadjoint senior term we can partially solve the problem having applied the results of the perturbation theory, within the framework of which the following papers are well-known [1]}, [2]}, [3]},
[4]},[5]},
[6]}. Generally, to apply the last paper results for a concrete operator \(L\)  we must be able to represent it by a sum \(L=T+A,\)  where the senior term
\(T\)  must be either a selfadjoint or normal operator. In other cases we can use methods of the papers
[7]},[8]} which are relevant if we deal with non-selfadjoint operators and allow us to study spectral properties of operators whether we have the mentioned above representation or not. We should add that the results of the paper [5]} can be also applied to study non-selfadjoin operators (see a detailed remark in [6]}).
